Ergodic Problems for Real Complex Systems in Chemical Physics

Komatsuzaki, Tamiki; Baba, Akinori; Kawai, Shinnosuke; Toda, Mikito; Straub, John E.; Berry, R. Stephen

doi:10.1002/9781118087817.ch5

Cited by 11 publications

(9 citation statements)

References 126 publications

(139 reference statements)

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“…There we find a clear boundary that divides the whole phase space into a region to bring the system to the reactant and that to the product. (One can refer to books 15,16 and papers 17-24, 26, 39 for the generalization to nonlinearly coupled multidimensional classical systems.) For the sake of completeness, we give a brief review of the Wigner-Weyl formalism of quantum mechanics in Sec.…”

Section: Theorymentioning

confidence: 99%

“…The other important building block of the phase space in determining the fate of the reaction are so-called invariant manifolds. 15,16 An invariant manifold is a set of phase space points such that, once the system is in that manifold, the system will stay in it perpetually. If the dimension of the manifold is less than that of the phase space by one, the manifold can divide the space into two disjoint regions.…”

Section: Introductionmentioning

confidence: 99%

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Quantum reaction boundary to mediate reactions in laser fields

Kawai

Komatsuzaki

2011

The Journal of Chemical Physics

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Dynamics of passage over a saddle is investigated for a quantum system under the effect of timedependent external field (laser pulse). We utilize the recently developed theories of nonlinear dynamics in the saddle region, and extend them to incorporate both time-dependence of the external field and quantum mechanical effects of the system. Anharmonic couplings and laser fields with any functional form of time dependence are explicitly taken into account. As the theory is based on the Weyl expression of quantum mechanics, interpretation is facilitated by the classical phase space picture, while no "classical approximation" is involved. We introduce a quantum reactivity operator to extract the reactive part of the system. In a model system with an optimally controlled laser field for the reaction, it is found that the boundary of the reaction in the phase space, extracted by the reactivity operator, is modulated with time by the effect of the laser field, to "catch" the system excited in the reactant region, and then to "release" it into the product region. This method provides new insights in understanding the origin of optimal control of chemical reactions by laser fields.

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Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum reaction boundary to mediate reactions in laser fields

Kawai

Komatsuzaki

2011

The Journal of Chemical Physics

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“…In other words, in an ergodic system an arbitrary function can be defined in a certain mathematical space within the phase space of the whole system, in which its characteristic becomes indistinguishable from the ensemble over all accessible points. 23 Expressing a higher degree of ergodicity can be understood as increasing the fraction of phase space in which its property time average characteristic becomes indistinguishable from the ensemble average for the distribution of all accessible points in the phase space of the system. Expressing a degree of nonergodicity is therefore not a proper term but a consequence of the degree of ergodicity.…”

Section: Introductionmentioning

confidence: 99%

Tailoring ergodicity through selective A-site doping in the Bi1/2Na1/2TiO3–Bi1/2K1/2TiO3 system

Acosta

Liu

Deluca

et al. 2015

Journal of Applied Physics

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Articles you may be interested inSolid-state conversion of (Na1/2Bi1/2)TiO3-BaTiO3-(K1/2Na1/2)NbO3 single crystals and their piezoelectric properties Appl. Phys. Lett. 104, 222910 (2014) The morphotropic phase boundary composition Bi 1/2 Na 1/2 TiO 3 -20 mol. % Bi 1/2 K 1/2 TiO 3 was chosen as initial material to do selective A-site aliovalent doping replacing Na and K by 1 at. % La, respectively. The materials were studied macroscopically by measuring dielectric and electromechanical properties. The Na-replaced material has a lower freezing temperature T fr , lower remanent polarization and remanent strain, and thus a higher degree of ergodicity than the K-replaced material. These results are contrasted with local poling experiments and hysteresis loops obtained from piezoresponse force microscopy. The faster relaxation of the tip-induced local polarization and the lower remanent state in bias-on and -off loops confirm the higher degree of ergodicity of the Na-replaced material. The difference in functional properties is attributed to small variations in chemical pressure achieved through selective doping. Raman results support this working hypothesis. V C 2015 AIP Publishing LLC.[http://dx

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“…In other words, in an ergodic system an arbitrary function can be defined in a certain mathematical space within the phase space of the whole system, in which the characteristic property´s time average becomes indistinguishable from the ensemble over all accessible points. 99,100 Expressing a higher degree of ergodicity can be understood as increasing the fraction of phase space in which its property time average characteristic becomes indistinguishable from the ensemble average for the distribution of all accessible points in the phase space of the system. Expressing a degree of non-ergodicity within a phase space is therefore not proper but a consequence of the degree of ergodicity.…”

Section: General Descriptionmentioning

confidence: 99%

Strain Mechanisms in Lead-Free Ferroelectrics for Actuators

Acosta

2016

Springer Theses

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Ergodic Problems for Real Complex Systems in Chemical Physics

Cited by 11 publications

References 126 publications

Quantum reaction boundary to mediate reactions in laser fields

Quantum reaction boundary to mediate reactions in laser fields

Tailoring ergodicity through selective A-site doping in the Bi1/2Na1/2TiO3–Bi1/2K1/2TiO3 system

Strain Mechanisms in Lead-Free Ferroelectrics for Actuators

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